Answer:
For the temperature to be below 32 F, following inequality must be met,
[tex]h\geq 9.333[/tex]
Step-by-step explanation:
Let "t" be the temperature at any time.
General format of a linear equation can be given as,
y= mx + c
Where,
y ⇒ dependent variable ( in this case temperature t)
m⇒ Gradient ( the rate at which the temperature drops)
x⇒ independent variable ( hours )
c⇒ intercept ( this is the starting temperature)
Now we can substitute the given values to the above format to arrive at the equation,
[tex]t=-3h+60[/tex]
We can re-arrange the equations as ,
[tex]3h=60-t[/tex]
=[tex]h=20-\frac{t}{3}[/tex]
We can write this as an inequality when t = 32 F
[tex]h\geq 20-\frac{32}{3}[/tex]
=[tex]h\geq \frac{28}{3}[/tex]
=[tex]h\geq 9.333[/tex]
On a recent day 8 euros were worth $9 and 24 euros were worth $27 write an equation of the form y equals kx to show the relationship between the number of euros and the value in dollars.
Answer:
y=8x/9
Step-by-step explanation:
Given that 8 euros were worth $9 and
24 euros were worth $27.
Let y represent the number of Euros and x no of dollars.
Given that the relation is of the form y = kx+C
When x=0 y =0,
i.e. C =0
Hence equation is of the form y = kx
Substitute x=8 and y =9
We get 9 = 8k
Or k =8/9
Hence relation is y=8x/9 is the relation between x and y.
WE can verify this for 27 dollars worth 24 euros.
24 =8/9(27) is true.
Thus equation is verified.
a company is planning to hire 12 new employees a simulation is run to determine 12 random birthdays using numbers to represent the days of the year (january 1 = 1 through december 31 = 365) based on the simulation what is the probability that a randomly selected employee will have a birthday in the first 100 days of the year?
344 180 274 358 64 121 32 96 151 275 93 49
(Please help and tell me how I do this)
Answers are
0.417
0.583
0.333
0.120
344 180 274 358 64 121 32 96 151 275 93 49
Out of the 12 numbers above, 5 (in bold type) are 100 or less.
5/12 = 0.41666...
Answer: 0.417
The probability that an employee selected randomly has a birthday in the first 100 days is 0.417
Recall :
Probability = required outcome / Total possible outcomes
Total possible outcomes :
344 180 274 358 64 121 32 96 151 275 93 49 = 12Required outcomes :
Values less Than or equal to 100 : 64, 96, 32, 93, 49 = 5Therefore,
P(first 100 days) = 5 / 12 = 0.41666Therefore, the selection probability is 0.417
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If John ran a 5 km marathon how long What is that in meters
Dillion divided a 3 1/3 pound bag of pears among his 5 friends. How many pounds of pears does did each friend revive?
Each friend received 10 ounces of pears after Dillion divided the 3 1/3 pound bag among them.
First, we need to convert the weight of the pears from pounds and thirds to decimal form.
To do this, we divide the 3 1/3 pounds by 16 (since there are 16 ounces in a pound):
3 1/3 pounds = 3 * (1 + 1/3) pounds = 3.333 pounds
Now we know that each friend received 3.333 pounds / 5 friends = .6666 pounds of pears. To convert this decimal into something more understandable, multiply it by 16 since there are 16 ounces in a pound:
.6666 pounds * 16 = 10 ounces
So, each friend received 10 ounces of pears.
Each friend received 10 ounces of pears after Dillion divided the 3 1/3 pound bag among them.
First, we need to convert the weight of the pears from pounds and thirds to decimal form.
To do this, we divide the 3 1/3 pounds by 16 (since there are 16 ounces in a pound):
3 1/3 pounds = 3 * (1 + 1/3) pounds = 3.333 pounds
Now we know that each friend received 3.333 pounds / 5 friends = .6666 pounds of pears. To convert this decimal into something more understandable, multiply it by 16 since there are 16 ounces in a pound:
.6666 pounds * 16 = 10 ounces
So, each friend received 10 ounces of pears.
find the ratio between a:b for each problem
1.) 2a=9b
2.) 6a-3b=5b
3.) a+b=3b
4.)a/5=b/7
1. 2a=9b first we will divide the both sides with parameter b and get
2(a/b)=9 now we will divide both sides with number 2 and get
a/b=9/2 => a : b = 9 : 2
2. 6a-3b=5b first we will add to both sides number (+3) and get
6a=5b+3b => 6a=8b then divide the both sides with parameter b and get
6(a/b)=8 now we will divide the both sides with number 6 and get
a/b=8/6 if we simplify the fraction we get
a/b=4/3 => a : b = 4 : 3
3. a+b=3b we will add to the both sides parameter (-b) and get
a=3b-b => a=2b then divide the both sides with parameter b and get
a/b=2 => a/b=2/1 => a : b = 2 : 1
4. a/5=b/7 first we will divide the both sides with paremeter b and get
a/(5b)=1/7 now we will multiply the both sides with number 5 and get
a/b=5/7 => a : b = 5 : 7
Good luck!!!
The ratio a:b in the four problems given are 9:2, 4:3, 2:1, and 5:7 respectively. This is achieved by isolating 'a' in each equation and simplifying the resulting expression.
Explanation:Let's find the ratio between a:b for each of the problems you've provided:
In the equation 2a = 9b, divide both sides by 2b to get a:b ratio. This gives a/b = 9/2, which simplifies to the ratio of a:b = 9:2.For the equation 6a - 3b = 5b, first add 3b to both sides to isolate 'a'. This gives 6a = 8b. Dividing by 6b, we get a/b = 8/6, which simplifies to a:b = 4:3.In the case of a + b = 3b, subtract 'b' from both sides, which gives a = 2b. The ratio of a to b is therefore a:b = 2:1.Lastly in the equation a/5 = b/7, cross-multiplication gives 7a = 5b. Dividing both sides by 7b results in a/b = 5/7, which means a:b = 5:7.Learn more about Finding ratios here:https://brainly.com/question/21138916
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In a right triangle the length of a hypotenuse is c and the length of one leg is a, and the length of the other leg is b, what is the value of b, if a=2 root3 , c=2b
In a right triangle, the sum of the squares of the legs is the square of the hypotenuse.
So, you would have
[tex] a^2+b^2=c^2 [/tex]
If you plug the values, you have
[tex] (2\sqrt{3})^2+b^2=(2b)^2 [/tex]
So, you end up with a quadric equation in b:
[tex] 12+b^2=4b^2 \iff 3b^2=12 \iff b^2=4 \iff b=2 [/tex]
So, the three sides are
[tex] a=2\sqrt{3},\ b=2,\ c=4 [/tex]
Which equation has the solution x = 3?
1 point
−4x + 6 − 3x = 12 − 2x − 3x
4x + 6 + 3x = 12 + 2x + 3x
4x + 6 − 3x = 12 − 2x − 3x
4x + 6 − 3x = 12x + 2x + 3x
A store decreased its price on a computer by $56 to $355. What was the original price?
A. $299
B. $411
C. $301
D. $421
The original price of the computer was $411. This was found by adding the reduction amount to the final price, i.e., $355 + $56.
Explanation:This question is concerned with a simple arithmetic operation. It's provided that the price of the computer was reduced by $56 to $355. The original price should thus be the markdown plus the final price.
Performing this calculation:
Add the amount of reduction ($56) to the current price ($355).
The solution is:
$355 (final price) + $56 (reduction) = $411 (original price)
Therefore, the original price of the computer was $411
So, option D is ($411) correct .
Learn more about Price Reduction Calculation here:https://brainly.com/question/20845830
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Bart lives 6 blocks from his grandparents. Melinda lives 8 blocks farther from her grandparents as Bart does . How many blocks does Melinda live from her grandfathers
Given that Bart and Melinda are grand children and Bart lives
6 blocks from his grand parents.
Also given that Melinda lives 8 blocks farther from her grandparents as Bart does .
This means Melinda lives 6+8 = 14 blocks from her grand father house
This question involves addition because farther as Bart does means , Melinda lives 8 +6 hence we get 14
Answer is: Melinda lives 14 blocks from her grandfathers
Amina used the quadratic formula to solve an equation. Her result shows two solutions that are complex numbers with imaginary parts. Which expression could be Amina's result?
The expression that could be Amina's result is [tex]x = \dfrac{12 \pm \sqrt{-8}}{4}[/tex]
Which expression could be Amina's result?
From the question, we have the following parameters that can be used in our computation:
The list of options
Also, we have that
Her result shows two solutions that are complex numbers with imaginary parts
This can be expressed as
[tex]x = \dfrac{a \pm i\sqrt{b}}{c}[/tex]
From the list of options, the expresion that are of the above form are
[tex]x = \dfrac{12 \pm \sqrt{-8}}{4}[/tex]
hence, the expression that could be Amina's result is [tex]x = \dfrac{12 \pm \sqrt{-8}}{4}[/tex]
Question
Amina used the quadratic formula to solve an equation. Her result shows two solutions that are complex numbers with imaginary parts. Which expression could be Amina's result?
larry is flying at an altitude of 3,000 feet above ground level. Ground level is 188 feet above sea level. If he descends 567 feet and then climbs 120 feet, how far above sea level is larry? A) 2,692 feet b) 2,741 feet c) 3,041 feet d) 3,259 feet
Larry is 2365 feet above sea level. Hope this helps :o
Answer: the answer is b 2,741 sorry im late
4/|p|+12=14.
Can you solve with the absolute value of p as a denominator?
Select the multiplication sentence that applies the commutative property of multiplication to the example.
Example: 5 × 8 = 40
A.
8 × 5 = 40
B.
10 × 4 = 40
C.
20 × 2 = 40
Answer : A
Example: 5 × 8 = 40
A. 8 × 5 = 40
the commutative property of multiplication allows us to multiply the numbers in any order without changing the product. In example we have 5 * 8 . When we change the order it becomes 8 * 5. So here applies commutative property of multiplication.
B. 10 × 4 = 40
the commutative property of multiplication allows us to multiply the numbers in any order without changing the product. In example we have 5 * 8 . When we change the order it becomes 8 * 5. So here it does not applies commutative property of multiplication.
C. 20 × 2 = 40
the commutative property of multiplication allows us to multiply the numbers in any order without changing the product. In example we have 5 * 8 . When we change the order it becomes 8 * 5. So here it does not applies commutative property of multiplication.
in the right triangle shown, ∠a=30° and ab = 12√3 how long is ac
Solution :
Given that in the right triangle , ∠A=30° and AB = 12√3 .
As the figure is missing and its not clearly mentioned that AB is the base or hypotenuse of the right triangle. So two cases arises-
Case 1: AB is the base for ∠A of the right triangle (as shown in figure 1).
As we know from the trigonometric ratio that, [tex]cos(\theta) = \frac{base}{hypotenuse}[/tex]
Here , AB is the base and AC is the hypotenuse , and ∠A=30°
[tex]\Rightarrow cos(30)=\frac{AB}{AC} \\\\\Rightarrow AC=\frac{AB}{cos(30)}[/tex]
The value of [tex]cos(30)=\frac{\sqrt{3} }{2}[/tex]
[tex]\Rightarrow AC=12\sqrt{3}\times\frac{2 }{\sqrt{3} }\\\\\Rightarrow AC=24[/tex]
Hence, AC is 24 unit long.
Case 2: AB is the hypotenuse for ∠A of the right triangle (as shown in figure 2).
As we know from the trigonometric ratio that, [tex]cos(\theta) = \frac{base}{hypotenuse}[/tex]
Here , AB is the hypotenuse and AC is the base, and ∠A=30°
[tex]\Rightarrow cos(30)=\frac{AC}{AB} \\\\\Rightarrow AC=AB\timescos(30)[/tex]
The value of [tex]cos(30)=\frac{\sqrt{3} }{2}[/tex]
[tex]\Rightarrow AC=12\sqrt{3}\times\frac{\sqrt{3}}{2}\\\\\Rightarrow AC=18[/tex]
Hence, AC is 18 unit long.
Given a function where one x-intercept of a parabola is (-4,0), what will be the new x-intercept if h is increased by 6?
(2, 0) would be the new x - intercept.
The equation of a parabola can be written in vertex form as:
y = a(x - h)² + k
Here, h represents the x-coordinate of the vertex. The x-intercepts of the parabola are the points where the parabola crosses the x-axis (i.e., where y = 0).
Given that one x-intercept is at (-4, 0), we know that x-intercepts are symmetrically located around the vertex. If the vertex's x-coordinate h is increased by 6, the entire parabola shifts horizontally to the right by 6 units.
Since the x-intercept is affected by the shift in the vertex:
Before the shift: one of the x-intercepts is at -4.
After the shift by h, the new x-intercept will be located 6 units to the right of the original intercept.
Therefore, the new x-intercept will be at:
-4 + 6 = 2
Locating Zeros of Polynomial Function:
Approximate the real zeros to the nearest tenth
we are given
[tex]f(x)=2x^4-x^3+x-2[/tex]
we can check each options
option-A:
-1,1
we can plug x=-1 and x=1 and check whethet f(x)=0
At x=-1:
[tex]f(-1)=2(-1)^4-(-1)^3+(-1)-2[/tex]
[tex]f(-1)=0[/tex]
At x=1:
[tex]f(1)=2(1)^4-(1)^3+(1)-2[/tex]
[tex]f(1)=0[/tex]
so, this is TRUE
option-B:
0,1
we can plug x=0 and x=1 and check whethet f(x)=0
At x=0:
[tex]f(0)=2(0)^4-(0)^3+(0)-2[/tex]
[tex]f(0)=-2[/tex]
At x=1:
[tex]f(1)=2(1)^4-(1)^3+(1)-2[/tex]
[tex]f(1)=0[/tex]
so, this is FALSE
option-C:
-2,-1
we can plug x=-2 and x=-1 and check whethet f(x)=0
At x=-2:
[tex]f(-2)=2(-2)^4-(-2)^3+(-2)-2[/tex]
[tex]f(-2)=36[/tex]
At x=-1:
[tex]f(-1)=2(-1)^4-(-1)^3+(-1)-2[/tex]
[tex]f(-1)=0[/tex]
so, this is FALSE
option-D:
-1,0
we can plug x=-1 and x=0 and check whethet f(x)=0
At x=-1:
[tex]f(-1)=2(-1)^4-(-1)^3+(-1)-2[/tex]
[tex]f(-1)=0[/tex]
At x=0:
[tex]f(0)=2(0)^4-(0)^3+(0)-2[/tex]
[tex]f(0)=-2[/tex]
so, this is FALSE
Please help asap 35 pts
its (a.) thats it try it
The regular nonagon has rotational symmetry of which angle measures? Check all that apply. 40° 45° 120° 240° 260° 320°
Answer:
The correct answers are 40, 120, 240, and 320
Step-by-step explanation:
.
Answer:
1 ,3 , 4, 6
Step-by-step explanation:
1750932 x 2355435 x Y= ? 50pts
Simplify as much as possible
1,750,932 x 2,355,435 = 4,124,206,515,420
4,124,206,515,420 x Y cannot be simplified anymore, therefore,
4,124,206,515,420 x Y is your answer
~Rise Above the Ordinary, Senpai
All we need to do here is simplify, since there is no given answer to y. The numbers you've provided are quite large, so I'd suggest just using a calculator, unless they're supposed to be decimals. The simplified answer to this is 412,320,615,420y.
Plz Answer ASAP...thx! (20 points)
Two airplanes left the same airport and arrived at the same destination at the same time. The first airplane left at 8:00 a.m. and traveled at an average rate of 496 miles per hour. The second airplane left at 8:30 a.m. and traveled at an average rate of 558 miles per hour. Let x represent the number of hours that the first plane traveled.
How many hours did it take the first plane to travel to the destination?
(Write an equation)
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!
Simplify.
(3x^2 + 2x + 7X^3) + (10x^2 + 6x + 9)
Combine all the like terms.
There is only one term with X^3 so that stays the same.
Add 3X^2 and 10x^2 to get 13x^2.
Add 2x and 6x to get 8x.
There is only one term with a variable, so that also stays the same.
Now place them in order from highest exponent to lowest:
7x^3 + 13x^2 + 8x + 9
The answer is A.
For which situation is the use of approximate numbers most appropriate?
A) preparing your yearly taxes
B) ordering programs for a high school musical
C) paying a cashier for a meal at a fast food restaurant
D) the maximum number of basketball players allowed on the court at a time
What is the next term in the sequence?
2, –4, 8, –16, . . .
–24
–32
32
24
The answer is 32 Why?
Because since it's getting added by times 2 for every number the number after 16 would be 32 when doing 16 x 2 and since the last number being -16 was negative the number after it would be positive, also if you want it more straight forward the 32 cannot be negative because when you times a negative with a positive you get a positive. Hope this helps!
Analyze the diagram below and complete the instructions that follow.
Find AEB.
2x+50=7x
50 = 5x
x = 10
2(10) + 50
20 + 50
= 70 degrees
Two cars pass on a straight highway while traveling in opposite directions. One car is traveling 6 miles per hour faster than the other car. After 1.5 hours the two cars are 159 miles apart. Find the speed of each car.
COME GET 50 POINTS!!
The data in the table represent the height of an object over time.
Which model best represents the data?
Letter choice answers get brainliest!
I think your answer is B.
Answer:
Quadratic, because the height increases and then decreases.
Step-by-step explanation:
In an exponential function, the graph will either increase or decrease over the entire domain. It does not change direction.
We can see from the table that the heights increase and then decrease; this means it cannot be an exponential function.
A quadratic function has a graph that is u-shaped. It will start out either increasing or decreasing, and then after the maximum or minimum is reached, it changes direction.
We can see from the table that this is what the heights do; this means it is a quadratic function.
The graph shows a car's value as a function of its age.
What was the value of the car in Year 2?
Enter your answer in the box. Do NOT enter a dollar sign or a comma in your answer.
What is the probability that a stamp chosen at random is a commemorative or a special delivery stamp?
Definitive: 0.38
Commemorative: 0.16
Semipostal: 0.2
Airmail: 0.08
Special Delivery: 0.18
A) 0.03
B) 0.18
C) 0.16
D) 0.34
Answer: Option 'D' is correct.
Step-by-step explanation:
Since we have given that
[tex]P(\text{ getting a commemorative stamp})=0.16[/tex]
and
[tex]P(\text{getting a special delivery stamp})=0.18[/tex]
So, we need to find,
[tex]P(\text{getting either a commemorative or a special delivery stamp})\\=P(\text{getting a commemorative stamp})+P({\text{ getting a special delivery stamp})[/tex]
(∵they are independent events .)
[tex]P(\text{getting either a commemorative or a special delivery stamp})\\=0.16+0.18\\=0.34[/tex]
So, option 'D' is correct.
875,932,461,160 what digit is in the hundred-millions place of this number.
The digit in the hundred millions place is 9.
Final answer:
The digit in the hundred-millions place of the number 875,932,461,160 is 7.
Explanation:
The digit in the hundred-millions place of the number 875,932,461,160 is 7. Let's break down the places of the number:
Ones: 0Tens: 6Hundreds: 1Thousands: 1Ten Thousands: 6Hundred Thousands: 4Millions: 2Ten Millions: 3Hundred Millions: 7So in the number 875,932,461,160, 7 is the digit in the hundred-millions place.
You wish to have $3000 in 2 years to buy a fancy new stereo system. How much should you deposit each quarter into an account paying 8% compounded quarterly?
Answer:
Deposit each quarter = $342.68
Step-by-step explanation:
Formula use in this problem:
[tex] FV=C\times \left [ \frac{(1+i)^n-1}{i} \right ]\times (1+i) [/tex]
Where,
FV is future value, FV=$3000
C is cash flow quarterly( need to find),C=?
I is rate of interest ( divide by 4), i=[tex] \frac{0.08}{4}=0.02 [/tex]
N number of cash flow, n=8
Substitute all these values into formula to solve for C
[tex] 3000=C\times \left [ \frac{(1+0.02)^8-1}{0.02} \right ]\times (1+0.02) [/tex]
[tex] C=\frac{3000\times 0.02}{[(1+0.02)^8-1]\times (1+0.02)}[/tex]
So, C=$342.68
Final answer:
To achieve $3000 in 2 years in an account with 8% interest compounded quarterly, you should deposit $364.11 each quarter.
Explanation:
To find out how much you need to deposit each quarter to have $3000 in 2 years in an account that pays 8% interest compounded quarterly, you would use the future value of a series formula given by:
S = R [((1 + i)^n - 1) / i]
Where:
S = the future value of the series (in this case, $3000)
R = the regular deposit amount per period (what we're solving for)
i = the interest rate per period (8% per year or 0.08 divided by 4 for quarterly = 0.02)
n = the total number of compounds over the period (2 years * 4 quarters/year = 8 compounds)
Plugging in our values:
$3000 = R [((1 + 0.02)^8 - 1) / 0.02]
$3000 = R * [((1.02)^8 - 1) / 0.02]
$3000 = R * 8.2432
So, solving for R, we get:
R = $3000 / 8.2432 = $364.11
Therefore, to have $3000 in 2 years with an account that pays 8% interest compounded quarterly, you need to deposit $364.11 at the start of each quarter.